共查询到20条相似文献,搜索用时 828 毫秒
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程峰 《数学物理学报(A辑)》2021,(1):126-141
该文考虑了参数化的液晶的不可压双曲型的Ericksen-Leslie方程.形式上,让参数消失该文证明了这个极限方程存在一个局部的经典解.更进一步,该文形式上得出一个关于这个参数化的液晶的双曲型方程和极限方程的解的误差估计,这对应的是关于它们的经典解在L2空间中的一个形式上的能量估计. 相似文献
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本文考虑具有初始跳跃的二阶双曲型方程初边值问题.首先给出解的导数估计.然后在一非均匀网格上构造了一个差分格式,最后在能量范数意义下证明了差分格式解的一致收敛性. 相似文献
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本文研究了一类具有非线性耗散项的高阶Kirchhoff型方程的初边值问题.通过构造稳定集讨论了此问题整体解的存在性,应用Nakao的差分不等式建立了解能量的衰减估计.在初始能量为正的条件下,证明了解在有限时间内发生blow-up,并且给出了解的生命区间估计. 相似文献
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研究了周期区域上平衡态附近Landau-Fermi-Dirac方程的Cauchy问题.利用宏观-微观分解以及局部的守恒律得到一致空间能量估计.接着结合对非线性碰撞算子的细致估计,推导了包含随时间演化的等价瞬时能量的非线性能量估计,进而得到一致的先验估计.最后通过局部存在性、一致的先验估计以及连续性技巧,得到了Landau-Fermi-Dirac方程平衡态附近整体光滑解的存在性. 相似文献
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本文在全空间中研究一类带阻尼的散焦型分数阶薛定谔方程的柯西问题,阻尼系数是依赖于时间的,并且可能在无穷处消失.我们借助单调算子理论得到了弱解的存在性;利用Strichartz估计以及压缩不动点定理得到了局部解的唯一性;利用精细的能量估计和下半连续性讨论建立了L~2和H~α∩Lp+2的能量衰减估计. 相似文献
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探讨了半带状区域上二维Poisson方程只含有一个空间变量的热源识别反问题.这类问题是不适定的,即问题的解(如果存在的话)不连续依赖于测量数据.利用Carasso-Tikhonov正则化方法,得到了问题的一个正则近似解,并且给出了正则解和精确解之间具有Holder型误差估计.数值实验表明Carasso-Tikhonov正则化方法对于这种热源识别是非常有效的. 相似文献
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本文讨论了来自于神经传播和具粘性效应的杆的纵振动问题的一类具非线性阻尼的拟线性双曲型方程的初边值问题解的存在唯一性。所用的方法是能量估计和Pazy的半解方法。 相似文献
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一类广义KdV—Burgers型方程的初边值问题 总被引:3,自引:0,他引:3
本文研究了一类带三阶粘性项的广义KdV-Burgers型方程的初边值问题,运用Galerkin逼近方法,结合能量估计,得到了问题整体解的存在性,正则性,唯一性和稳定性等结果,并在一定条件下讨论了问题的解的渐边行为和“爆破”现象。 相似文献
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E. A. Kalita 《Ukrainian Mathematical Journal》1992,44(10):1235-1245
For second-order elliptic systems with the natural energy space W2
1 solutions with an isolated singularity are considered. If the speed of growth of the solution is less than the limiting speed determined by the modulus of the elliptic system, it is proved that either the singularity is removable or its order coincides with the order of the singularity of the fundamental solution of Laplace's equation. Systems are also considered with positive nonlinear lowest terms, for which a complete classification is obtained of the possible orders of isolated singularities.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1349–1358, October, 1992. 相似文献
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建立了二阶抛物型方程组的一种新数值方法-再生核函数法.利用再生核函数,直接给出了每个离散时间层上近似解的显式表达式,由显式表达式可实现完全并行计算;用能量估计法证明了格式的稳定性及二阶收敛性;给出了一些数值结果. 相似文献
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Hesheng Sun 《偏微分方程(英文版)》1999,12(2):106-110
In this paper a nonliuear system of second order equations of mixed type is considered. The existence of H¹ strong solution for the modified Tricomi problem is proved by the energy integral method and the Leray-Schauder's fixed point principle. 相似文献
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Xiu Ye & Shangyou Zhang 《高等学校计算数学学报(英文版)》2023,16(1):230-241
In this paper, we introduce a stabilizer free weak Galerkin (SFWG) finite
element method for second order elliptic problems on rectangular meshes. With
a special weak Gradient space, an order two superconvergence for the SFWG finite
element solution is obtained, in both $L^2$ and $H^1$ norms. A local post-process lifts
such a $P_k$ weak Galerkin solution to an optimal order $P_{k+2}$ solution. The numerical
results confirm the theory. 相似文献
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Yiheng Wei Bin Du Songsong Cheng Yong Wang 《Journal of Optimization Theory and Applications》2017,174(1):122-138
This paper deals with the time-optimal control problem for a class of fractional order systems. An analytic solution of the time-optimal problem is proposed, and the optimal transfer route is provided. Considering it is usually adopted in the discrete situation for actual control system, the sampling date may induce chattering phenomenon, an alternative sub-optimal solution is constructed. Additionally, the special and meaningful application of fractional order tracking differentiator is introduced to explain our main results. The effectiveness and advantages of the proposed method have been illustrated by numerical examples. 相似文献
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Sun Hesheng 《偏微分方程(英文版)》1993,6(2)
A system of first order equations of mixed type, which may be reduced to a general second order equation of mixed type, is considered. Uniqueness of solution to the generalized Tricomi problem is proved by the method of auxiliary function. Existence of H¹ strong solution is based on a characteristic problem and is proved by the Fredholm's alternative properties. 相似文献
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Anders Rønne Rassmusen Mads Peter Sørensen Yuri Borisovich Gaididei Peter Leth Christiansen 《Acta Appl Math》2011,115(1):43-61
A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless
case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical
equations. Thus it preserves the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear
acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity
potential. Numerical studies of the evolution of a number of arbitrary initial conditions as well as head-on colliding and
confluent wave fronts exhibit several nonlinear interaction phenomena. These include wave fronts of changed velocity and amplitude
along with the emergence of rarefaction waves. An analysis using the continuity of the solutions as well as the boundary conditions
is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance
equation. 相似文献
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Lena Wunderlich 《PAMM》2006,6(1):775-776
We consider the numerical treatment of systems of second order differential-algebraic equations (DAEs). The classical approach of transforming a second order system to first order by introducing new variables can lead to difficulties such as an increase in the index or the loss of structure. We show how we can compute an equivalent strangeness-free second order system using the derivative array approach and we present Runge-Kutta methods for the direct numerical solution of second order DAEs. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Samer Israwi 《偏微分方程(英文版)》2020,33(3):261-274
In this paper, a generalized nonlinear dissipative and dispersive equation
with time and space-dependent coefficients is considered. We show that the control of
the higher order term is possible by using an adequate weight function to define the
energy. The existence and uniqueness of solutions are obtained via a Picard iterative
method. As an application to this general Theorem, we prove the well-posedness of
the Camassa-Holm type equation. 相似文献
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A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results. 相似文献